Currently Large Language Models (LLM) coupled with Rienforcement Learning with Verifiable Rewards (RLVR) are winning math olympiads, proving theorems etc. which is to be expected, because you have Lean in math, but not the equivallent in physics. I suspect at least in short-term LLMs are unable to gain “true” physical intuition, at least not in the sense that giants like Einstein had. Nonetheless this is a collection of physics arguments framed around the reasoning that makes a strange result feel inevitable once you see it the “right way”.

1. The starting intuition, and why it’s too strong as stated # Gödel’s incompleteness theorems show that any sufficiently expressive, consistent formal system \$F\$ contains a true statement \$G\$ it cannot prove from its own axioms — informally, $$ G \leftrightarrow \neg \mathrm{Provable}_F(G). $$ It’s tempting to reach for an analogy: what if consciousness is a real physical phenomenon whose complete truth can’t be derived from whatever formal or mathematical framework we use to describe physical reality?

This is a companion piece to Consciousness, Computability, Decidability, and Evolvability. That piece argued for attacking weaker, well-formed questions about consciousness-adjacent proxies instead of the metaphysical question directly, and singled out evolvability as the more empirically checkable of the two tracks, since a negative evolvability result can be tested against biology in a way a negative decidability result cannot. This piece works through what that actually looks like as a formal object, and what a controllable synthetic world buys you when trying to study it.

Large language models are experiencing their Cambrian explosion. They may not be the path to AGI, but at least they give a taste of what it could be. The current mainstream approach to rely on scaling, may not be the sole solution, as the data runs out, and the models are plateauing in benchmarks, though we may very well see emergent behaviors that surprise us, as the bitter lesson taught us. In this article, I first review Transformers model, then summarize useful workflows with LLMs, which I intend to keep updating.

Essentially all modern processors have the capability to apply instructions on a vector in one processing unit cycle instead of operating on a single scalar. Language designers and compiler developers have been trying hard to leverage these hardware capabilities by compiling scalar programs into vector instructions. One possible approach is using SIMD (Single Instruction, Multiple Data) intrinsics, supported by all modern C/C++ compilers, through SSE (Streaming SIMD Extension), AVX (Advanced Vector Extensions) others for x86 architectures, and ARM NEON extensions.